Find the maximum value of function f (x) = SiNx + cosx + SiNx * cosx

Let SiNx + cosx = X
2sinx*cosx=(sinx+cosx)^2-1=x^2-1
y=sinx+cosx+sinx*cosx=(x^2-1)/2+x=1/2(x+1)^2-1
x=sinx+cosx=√2sinx(x+π/2)
∴x∈[-√2,√2]
When x = - 1, y has a minimum value of - 1
When x = √ 2, y has a maximum value of 2 + √ 2
The range of y = SiNx + cosx + SiNx * cosx is - 1

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